Adept: A fast automatic differentiation library for C++

Adept (Automatic Differentiation using Expression Templates) is a
software library that enables algorithms written in C and C++ to
be automatically
differentiated. It uses an operator overloading approach, so
very little code modification is required. Differentiation can be
performed in forward mode, reverse mode (to compute the adjoint),
or the full Jacobian matrix can be computed. Moreover, the way that
expression
templates have been used and several other important
optimizations mean that reverse-mode differentiation is
significantly faster than other libraries that provide equivalent
functionality
(ADOL-C, CppAD
and Sacado)
and less memory is used. In fact, Adept is also often only around
10-25% slower than an adjoint code you might write by hand, but
immeasurably faster in terms of user time; adjoint coding is very
time consuming and error-prone. For further details,
read the Adept paper below.

News

Adept 1.1 is now
on GitHub! (June
2015) The new version has a more permissive license, supports OpenMP
parallelization of the calculation of Jacobian matrices, has better
Windows support and is accompanied by a new mailing list.

Functionality

Adept provides the following functionality:

Full Jacobian matrix. Given the non-linear
function y=f(x) coded in C or C++, Adept will
compute the matrix H=∂y/x, where the
element at row i and column j of H
is Hi,j=∂yi/∂xj. This
matrix will be computed much more rapidly and accurately than if you
simply recompute the function multiple times perturbing each element
of x one by one. The Jacobian matrix is used in
the Gauss-Newton
and Levenberg-Marquardt
minimization algorithms.

Reverse-mode differentiation. This is a key component in
optimization problems where a non-linear function needs to be
minimized but the state vector x is too large for it to make
sense to compute the full Jacobian matrix. Atmospheric data
assimilation is the canonical example in Meteorology. Given a
non-linear function y=f(x) and a vector of
adjoints ∂J/∂y (where J is the scalar
function to be minimized), Adept will compute the vector of adjoints
∂J/∂x. Formally,
∂J/∂x is given by the matrix-vector
product HT∂J/∂y, but it is
computed here without computing the full Jacobian
matrix H. The adjoint may then be used in
a quasi-Newton
minimization scheme.

Forward-mode differentiation. Given the non-linear
function y=f(x) and a vector of perturbations
δx, Adept will compute the corresponding vector
δy arising from a linearization of the
function f. Formally, δy is given by the
matrix-vector product Hδx, but it is computed
here without computing the full Jacobian matrix H. Note that
Adept is optimized for the reverse case, so might not be as fast
(and will certainly not be as economical in memory) in the forward
mode as libraries written especially for that purpose.

Note that at present Adept is missing some functionality that you
may require:

Differentiation is first-order only: it cannot directly compute
higher-order derivatives such as the Hessian matrix.

Limited support for complex numbers; no support for mathematical
functions of complex numbers, and expressions involving operations
on complex numbers are not optimized.

Your code must only operate on variables individually: they can be
stored in C-style arrays or std::vector types, but Adept
does not work fully with containers that allow operations on entire
arrays such as the std::valarray type.

C and C++ only; this library could not be written in Fortran since
the language provides no template capability.

Windows support via the capability to compile code to be
differentiated without the need to link to an external library.

More test programs and a benchmarking tool.

Version 1.0:adept-1.0.tar.gz (3
September 2013). The main changes since version 0.9 are:

LIFO requirement removed in allocation of active objects in
memory: more efficient for codes that don't deallocate objects in
the reverse order from their allocation.

Interface change: independent variables no longer need to be
initialized using set_value; they can now be initialized
using the ordinary assignment operator (=) provided that
the new_recording function is called immediately after
they are initialized (see section 5.2 of the User Guide).

Ability to interface to code components that compute their own
Jacobian (e.g. those written in Fortran).

More test programs, including one that interfaces to
the GNU Scientific
Library to perform a real minimization.

C++ exceptions are thrown when an error occurs.

Recording of derivative information can be "paused" so that the
same function can be called from within the program both with and
without automatic differentiation.

Source code can be compiled twice to produce two versions of a
function, one with automatic differentiation and one without.

If you use the code and have any comments, queries, requests or
bug-fixes then please
contact Robin Hogan. You
can also post to
the mailing
list. I also welcome emails to tell me how Adept is being used.

License and copyright

Adept is dual-licensed, which means that you may choose to
be bound by either of the following licenses.

The
Apache License, Version 2.0. This is a permissive,
free-software license that will be the choice for almost all users.
It permits you to use and modify the library for any purpose, and to
redistribute it under the same terms. Modified versions, or
derivative works incorporating Adept, may be distributed in source
or object form with a few restrictions that are stated in the
license, but provided these conditions are met it may be
incorporated into proprietary software.

The ESA Software Community License (ESCL), Type
1. Recognising that Adept was written largely with funding from
the European Space Agency, you may alternatively use the Type-1
ESCL. It is more restrictive than Apache 2.0 in that derivative
works can only be released under the same license, and the license
is limited to users in ESA's Member States. The latter condition
means that it is not an open-source license. There are several
versions of the Type-1 ESCL in circulation; you may use any official
version sanctioned by ESA.

In addition to choosing only one of the two licenses above, you are
permitted to dual-license your own derivative work using the same two
licenses, if you prefer.

Acknowledgements

Adept 1.0 was developed by Robin Hogan with funding
from European Space Agency contract
40001041528/11/NL/CT.